Table Of ContentP S
OWER YSTEM
E
NGINEERING
Second Edition
About the Authors
D P Kothari is Professor, Centre for Energy Studies,
Indian Institute of Technology, Delhi. He has
been Head of the Centre for Energy Studies
(1995–97) and Principal (1997–98) Visvesvaraya
Regional Engineering College, Nagpur. He has
been Director-incharge, IIT Delhi (2005), Deputy
Director (Admn.) (2003–2006). Earlier (1982–83
and 1989), he was a visiting fellow at RMIT,
Melbourne, Australia. He obtained his BE, ME and
Ph.D degrees from BITS, Pilani. A fellow of the
Institution of Engineers (India), fellow of National Academy of Engineering,
fellow of National Academy of Sciences, Senior Member IEEE, Member IEE,
Life Member ISTE, Professor Kothari has published/presented around 500
papers in national and international journals/conferences. He has authored/co-
authored more than 18 books, including Power System Optimization, Modern
Power System Analysis, Electric Machines, Power System Transients, Theory
and Problems of Electric Machines and Basic Electrical Engineering. His
research interests include power system control, optimization, reliability and
energy conservation. He has received the National Khosla award for Lifetime
Achievements in Engineering for 2005 from IIT Roorkee.
I J Nagrath is Adjunct Professor, BITS, Pilani, and
retired as Professor of electrical engineering and
Deputy Director of Birla Institute of Technology
and Science, Pilani. He obtained his BE with Hons.
in electrical engineering from the University of
Rajasthan in 1951 and MS from the University of
Wisconsin in 1956. He has co-authored several
successful books which include Electric Machines,
Modern Power System Analysis and Systems:
Modelling and Analysis. He has also published
several research papers in prestigious national and international journals.
Other books by the same authors
978 007 0435896 KOTHARI & NAGRATH Basic Electrical Engineering, 2e
978 007 0583771 KOTHARI & NAGRATH Electric Machines, 3e
978 007 0494893 KOTHARI & NAGRATH Modern Power System Analysis, 3e
978 007 0616660 KOTHARI & NAGRATH Electric Machines (Sigma Series)
P S
OWER YSTEM
E
NGINEERING
Second Edition
D P KOTHARI
Professor, Centre for Energy Studies
Former Deputy Director (Admn.)
Indian Institute of Technology
New Delhi
Former Principal, V.R.C.E., Nagpur
Former Director-Incharge, IIT Delhi
I J NAGRATH
Adjunct Professor, BITS
Professor of Electrical Engineering and Deputy Director (Retd.)
Birla Institute of Technology and Science
Pilani
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Power System Engineerng, 2e
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RBXCRRQYDDQCD
To my wife
Shobha
—D P Kothari
To my wife
Pushpa
—I J Nagrath
Contents
Preface to the Second Edition xv
Preface to the First Edition xvii
1. Introduction 1
1.1 Electric Power System 1
1.2 Indian Power Sector 2
1.3 A Contemporary Perspective 2
1.4 Structure of Power Systems 14
1.5 Conventional Sources of Electric Energy 16
1.6 Magnetohydrodynamic (MHD) Generation 35
1.7 Geothermal Energy 36
1.8 Environmental Aspects of Electric Energy Generation 37
1.9 Renewable Energy Resources 42
1.10 Solar Energy and its Utilization 43
1.11 Wind Power 59
1.12 Biofuels 66
1.13 Generating Reserve, Reliability and Certain Factors 67
1.14 Energy Storage 71
1.15 Energy Conservation 75
1.16 Growth of Power Systems in India 77
1.17 Deregulation 79
1.18 Distributed and Dispersed Generation 82
1.19 Power System Engineers and Power System Studies 83
1.20 Use of Computers and Microprocessors 83
1.21 Problems Facing Indian Power Industry and its Choices 84
Annexure 1.1 87
Annexure 1.2 87
2. Inductance and Resistance of Transmission Lines 95
2.1 Introduction 95
2.2 Definition of Inductance 95
2.3 Flux Linkages of an Isolated Current-Carrying Conductor 96
2.4 Inductance of a Single-Phase Two-Wire Line 100
2.5 Conductor Types 102
2.6 Flux Linkages of One Conductor in a Group 103
viii Contents
2.7 Inductance of Composite Conductor Lines 104
2.8 Inductance of Three-Phase Lines 109
2.9 Double-Circuit Three-Phase Lines 116
2.10 Bundled Conductors 119
2.11 Resistance 121
2.12 Skin Effect and Proximity Effect 122
2.13 Magnetic Field Induction 123
2.14 Summary 123
3. Capacitance of Transmission Lines 127
3.1 Introduction 127
3.2 Electric Field of a Long Straight Conductor 127
3.3 Potential Difference between Two Conductors of a Group of
Parallel Conductors 128
3.4 Capacitance of a Two-Wire Line 129
3.5 Capacitance of a Three-Phase Line with Equilateral
Spacing 131
3.6 Capacitance of a Three-Phase Line with Unsymmetrical
Spacing 132
3.7 Effect of Earth on Transmission Line Capacitance 134
3.8 Method of GMD (Modified) 142
3.9 Bundled Conductors 142
3.10 Electrostatic Induction 143
3.11 Summary 143
4. Representation of Power System Components 146
4.1 Introduction 146
4.2 Single-Phase Representation of Balanced Three-Phase
Networks 146
4.3 The One-Line Diagram and the Impedance or Reactance
Diagram 148
4.4 Per Unit (PU) System 150
4.5 Complex Power 156
4.6 The Steady State Model of Synchronous Machine 159
4.7 Power Transformer 172
4.8 Transmission of Electric Power 172
4.9 System Protection 172
4.10 Representation of Loads 174
4.11 Summary 175
5. Characteristics and Performance of Power Transmission Lines 177
5.1 Introduction 177
5.2 Short Transmission Line 178
5.3 Medium Transmission Line 186
5.4 The Long Transmission Line—Rigorous Solution 188
Contents ix
5.5 The Equivalent Circuit of a Long Line 192
5.6 Interpretation of the Long Line Equations 198
5.7 Ferranti Effect 204
5.8 Tuned Power Lines 206
5.9 Power Flow Through a Transmission Line 207
5.10 Methods of Voltage Control 223
5.11 Summary 231
6. Load Flow Studies 235
6.1 Introduction 235
6.2 Network Model Formulation 237
6.3 Formation of YBUS by Singular Transformation 247
6.4 Load Flow Problem 253
6.5 Gauss–Siedel Method 263
6.6 Newton–Raphson Method 274
6.7 Decoupled Load Flow Studies 290
6.8 Comparison of Load Flow Methods 301
6.9 Control of Voltage Profile 303
6.10 Load Flow under Power Electronic Control 312
6.11 Summary 318
7. Optimal System Operation 331
7.1 Introduction 331
7.2 Optimal Operation of Generators on a Bus Bar 332
7.3 Optimal Unit Commitment (UC) 345
7.4 Reliability Considerations 349
7.5 Optimal Generation Scheduling 354
7.6 Optimal Load Flow Solution 368
7.7 Optimal Scheduling of Hydrothermal System 376
7.8 Power System Security 383
7.9 Maintenance Scheduling (MS) 389
7.10 Power-System Reliability 389
7.11 Summary 394
Annexure 7.1 402
8. Automatic Generation and Voltage Control 409
8.1 Introduction 409
8.2 Load Frequency Control (Single Area Case) 410
8.3 Load Frequency Control and Economic Despatch Control 424
8.4 Two-Area Load Frequency Control 425
8.5 Optimal (Two-Area) Load Frequency Control 431
8.6 Automatic Voltage Control 437
8.7 Load Frequency Control with Generation Rate Constraints
(GRCs) 439
8.8 Speed Governor Dead-Band and its Effect on AGC 440
x Contents
8.9 Digital LF Controllers 441
8.10 Decentralized Control 442
8.11 Discrete Integral Controller for AGC 443
8.12 AGC in a Restructured Power System 443
8.13 Summary 449
9. Symmetrical Fault Analysis 453
9.1 Introduction 453
9.2 Transient on a Transmission Line 454
9.3 Short Circuit of a Synchronous Machine 456
9.4 Short Circuit of a Loaded Synchronous Machine 465
9.5 Selection of Circuit Breakers 470
9.6 Algorithm for Short Circuit Studies 475
9.7 ZBUS Formulation 480
9.8 Summary 489
10. Symmetrical Components 495
10.1 Introduction 495
10.2 Symmetrical Component Transformation 496
10.3 Phase Shift in Star-Delta Transformers 502
10.4 Sequence Impedances of Transmission Lines 505
10.5 Sequence Impedances and Sequence Network of
Power System 507
10.6 Sequence Impedances and Networks of Synchronous
Machine 507
10.7 Sequence Impedances of Transmission Lines 511
10.8 Sequence Impedances and Networks of Transformers 512
10.9 Construction of Sequence Networks of a Power System 515
10.10 Summary 519
11. Unsymmetrical Fault Analysis 523
11.1 Introduction 523
11.2 Symmetrical Component Analysis of Unsymmetrical Faults 524
11.3 Single Line-to-Ground (LG) Fault 525
11.4 Line-to-Line (LL) Fault 528
11.5 Double Line-to-Ground (LLG) Fault 530
11.6 Open Conductor Faults 540
11.7 Bus Impedance Matrix Method for Analysis of Unsymmetrical
Shunt Faults 542
11.8 Summary 552
12. Power System Stability 558
12.1 Introduction 558
12.2 Dynamics of a Synchronous Machine 560
12.3 Power Angle Equation 565
Contents xi
12.4 Node Elimination Technique 570
12.5 Simple Systems 577
12.6 Steady State Stability 579
12.7 Transient Stability 584
12.8 Equal Area Criterion 586
12.9 Numerical Solution of Swing Equation 605
12.10 Multimachines Stability 612
12.11 Some Factors Affecting Transient Stability 622
12.12 Summary 631
13. Power System Transients 635
13.1 Introduction 635
13.2 Types of System Transients 635
13.3 Traveling Waves and Propagation of Surges 637
13.4 Generation of Overvoltages on Transmission Lines 658
13.5 Protection of Transmission Lines Against Lightning 661
13.6 Protection of Power System Apparatus Against Surges 663
13.7 Insulation Coordination 668
13.8 Lightning Phenomena 673
13.9 Neutral Grounding 676
13.10 Summary 679
14. Circuit Breakers 682
14.1 Circuit Breaking Transients 682
14.2 Circuit Breaker Rating 694
14.3 Arc and Arc Extinction 695
14.4 Circuit Breaker Types 699
14.5 HVDC Circuit Breakers 712
14.6 Testing of HVAC Circuit Breakers 715
14.7 Isolators 719
14.8 Fuses 720
14.9 Contactors 720
14.10 Summary 721
15. Power System Protection 723
15.1 Introduction 723
15.2 Protective Zones 724
15.3 Relaying Elements and Quantities 726
15.4 Current and Voltage Transformers 728
15.5 Relay Types and Characteristics 734
15.6 Relay Hardware 746
15.7 Relay Connections 761
15.8 Protection of Transmission Lines 767
15.9 Generator/Motor Protection 785
15.10 Transformer Protection 791
